Question

If x varies inversely as y and directly as t, and x = 12 when t = 10 and y = 25, find y when x is 6 and t = 3.


9 3/5
15
166 2/3

Answer 1

The first step is to create your model.

Answer 2

Looks like x = k*t*(1/y)

Answer 3

You are given values for x, t, and y so that you can solve for k.

Answer 4

Are you with me?

Answer 5

not sure....

Answer 6

What is giving you difficulty?

Answer 7

the solve for k....how should i do it???

Answer 8

You are given a word problem that you need to use to create a model.
Your problem says x increases directly with t and inversely with y.
Start with a general equation that grows directly with t and inversely (1/y) with y.

Answer 9

The general equation described above is x = k*t*(1/y)
This simple expression is useful because it generally describes all situations where x and y are inversely related and x and t are directly related.

Your question goes into more detail giving you values of x, y, and t so that you can solve for the constant factor k.

Answer 10

Step one is to setup the model
\[x = kt(\frac{ 1 }{ y })\]
Step 2 is to plug in x = 12 when t = 10 and y = 25 and solve for k.

Are you with me?

Answer 11

ok like this....12=k*10(1/25)

Answer 12

Yes! :-)

Answer 13

but what is the first step to solve for k???

Answer 14

use arithmetic to get k isolated so that you have # = k

Answer 15

I guess the first step would be to multiply both sides by 25.

Answer 16

like this...25*12=k*10*1/25*25
25*12=k*10

Answer 17

right

Answer 18

what should i do next???

Answer 19

divide both sides by 10

Answer 20

which =30????

Answer 21

Very good. Now step 3 is to take the second set of x's t's and (along with k) use the model equation to solve for y.

Answer 22

ok..

Answer 23

gat it is it 15???

Answer 24

:-D
Nice job!

Answer 25

thankx for ur help and time...:)

Answer 26

You are welcome.
Study hard!